Extrusion method for three dimensional modeling

ABSTRACT

A multi-tip extrusion method and apparatus for building a three-dimensional object deposits modeling materials from distinct supply sources, each in a layerwise predetermined pattern, from dispensers having co-planar dispensing tips. The tip spacing is controlled so that a road of material extruded by a leading one of the tips will cool and shrink from the plane of the tips before a trailing one of the tips passes over the road. In this manner, smearing of the road by a trailing one of the tips is avoided.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a divisional of application Ser. No. 09/845,566, filed Apr. 30, 2001, now U.S. Pat. No. 6,749,414 which is hereby incorporated by reference as if set forth fully herein.

BACKGROUND OF THE INVENTION

This invention relates to the fabrication of three-dimensional objects using extrusion-based layered manufacturing techniques. More particularly, the invention relates to forming three-dimensional objects from multiple types of modeling materials that are extruded in a flowable state and solidify after being deposited onto a base.

Three-dimensional models are used for functions including aesthetic judgments, proofing the mathematical CAD model, forming hard tooling, studying interference and space allocation, and testing functionality. Extrusion-based layered manufacturing machines build up three-dimensional models by extruding solidifiable modeling material from a nozzle tip carried by an extrusion head onto a base. “Wetting” of the base by the extruded material serves to separate the modeling material from the tip. Movement of the extrusion head with respect to the base is performed in a predetermined pattern under computer control, in accordance with design data provided from a computer aided design (CAD) system. Examples of extrusion-based apparatus and methods for making three-dimensional objects are described in Valavaara U.S. Pat. No. 4,749,347, Crump U.S. Pat. No. 5,121,329, Crump U.S. Pat. No. 5,340,433, Crump et al. U.S. Pat. No. 5,503,785, Danforth, et al. U.S. Pat. No. 5,900,207, Batchelder, et al. U.S. Pat. No. 5,764,521, Swanson U.S. Pat. No. 6,004,124, Stuffle et al. U.S. Pat. No. 6,067,480 and Batchelder, et al. U.S. Pat. No. 6,085,957, all of which are assigned to Stratasys, Inc., the assignee of the present invention.

In the Stratasys FDM® three-dimensional modeling machines of the current art, the CAD design of an object is “sliced” into multiple horizontal layers by a software program. The machines then built up the object layer-by-layer by extruding modeling material in fluent strands, termed “roads”. Each extruded road has a thickness equal to the height of a slice. The material being extruded fuses to previously deposited material and solidifies upon a drop in temperature to form a three-dimensional object resembling the CAD model. The modeling material is typically a thermoplastic or wax material. Alternatively, other types of materials, such as metals, which become flowable when heated, which solidify upon a drop in temperature, and which adhere to the previous layer with an adequate bond upon solidification can be employed.

In an extrusion-based modeling system, modeling material is supplied to the extrusion head as a feedstock of either a liquid or a solid material. Where the feedstock of modeling material is in solid form, a liquifier brings the feedstock to a flowable temperature for deposition. One technique is to supply modeling material in the form of a filament strand. Solid material feedstocks may alternatively be in the form of wafers, rods, slugs, or the like. A pressurization means is used to extrude molten modeling material from the extrusion head.

In modeling systems that employ a filament feed, modeling material is loaded into the machine as a flexible filament wound on a supply spool, such as disclosed in U.S. Pat. No. 5,121,329. The extrusion head, which includes the liquifier and a dispensing nozzle, receives the filament, melts the filament in the liquifier, and extrudes molten modeling material from the nozzle. Typically, the filament has a small diameter, such as on the order of 0.070 inches. A pair of motor-driven feed rollers on the extrusion head controllably advance the filament strand into the liquifier, which is heated so as to melt the filament. The liquifier is pressurized by the “pumping” of the strand of filament into the liquifier by the feed rollers. The strand of filament itself acts as a piston, creating a “liquifier pump”. The pressurization extrudes the molten modeling material out of an orifice of the nozzle at a volumetric flow rate, where it is deposited onto a base. The volumetric flow rate is a function of the size of the dispensing orifice and the rate of rotation of the feed rollers. By selective control of the feed-roller motor, the rate of advancement of the strand of filament, and thus the volumetric dispensing rate of the molten modeling material, can be closely controlled. A controller controls movement of the extrusion head in a horizontal x, y plane, controls movement of the base in a vertical z-direction, and controls the rate at which the feed rollers advance filament into the head. By controlling these processing variables in synchrony, the modeling material is deposited in roads at a desired flow rate, layer-by-layer, in areas defined from the CAD model. The dispensed material fuses and solidifies to form a three-dimensional object resembling the CAD model.

In building a model from a modeling material that thermally solidifies upon a drop in temperature, the modeling base is contained within a temperature-controlled build envelope. The build envelope is preferably a chamber which is heated to a temperature higher than the solidification temperature of the modeling material during deposition, and then gradually cooled to relieve stresses from the material. As disclosed in U.S. Pat. No. 5,866,058, this approach anneals stresses out of the model while it is being built so that the finished model is stress free and has very little distortion.

In creating three-dimensional objects by depositing layers of solidifiable material, supporting layers or structures are built underneath overhanging portions or in cavities of objects under construction, which are not supported by the modeling material itself. For example, if the object is a model of the interior of a subterranean cave and the cave prototype is constructed from the floor towards the ceiling, then a stalactite will require a temporary support until the ceiling is completed. A support structure may be built utilizing the same deposition techniques and apparatus by which the modeling material is deposited. The apparatus, under appropriate software control, produces additional geometry acting as a support structure for the overhanging or free-space segments of the object being formed. Support material may be dispensed in a like fashion as the modeling material and in coordination with the dispensing of the modeling material, to build up supporting layers or a support structure for the object. Support material is deposited either from a separate dispensing head within the modeling apparatus, or by the same dispensing head that deposits modeling material. A support material is chosen that will adhere to the modeling material during construction, and that is removable from a completed object. Various combinations of modeling and support materials are known, such as are disclosed in U.S. Pat. No. 5,503,785.

To accommodate the dispensing of two different materials, the above-mentioned '329 patent discloses a dispensing head having multiple supply passages into which materials of different compositions may be directed, with each passage terminating in a separate dispensing orifice. The dispensing orifices of the '329 patent are arranged on a single broad-based nozzle tip, as shown in FIG. 11 thereof. Experimentation with broad-faced dispensing has tips taught, however, that a broad-faced tip drags against the road being extruded and smears out object features. Object corners are particularly problematic. If a corner does not get out from under a tip face before the tip changes directions, the tip face will drag against the corner. As the outer diameter of the tip face increases, the corner radius will increase as well, so that a narrow deposited road no longer makes fine features.

To overcome the feature smearing problems of multiple orifices, the above-mentioned '785 patent teaches an extrusion head having independent nozzle tips. The apparatus of the '785 patent uses an electromechanical method to move one tip higher or lower than the other, so that only the tip through which material is being extruded will contact the part surface. While the apparatus of the '785 patent eliminates smearing problems, it introduces significant issues of alignment and calibration. Z-axis calibration of the tips must be verified, as well as X and Y offset calibration. Calibration requirements decrease throughput and reliability. The mechanical complexity of toggling the two tips additionally lowers reliability and increases cost of the machine.

Two other methods for accommodating the dispensing of two different materials are also known: (1) providing two extrusion heads, each including one dispenser for receiving and dispensing one of the modeling materials (such as is disclosed in the '124 patent); and (2) providing a single extrusion head that dispenses two materials through a single orifice in a common dispensing tip, each material being provided to the tip from a separate flow path in the extrusion head (such as is shown in FIG. 6 of the '329 patent). These methods have disadvantages as well. Where two extrusion heads are provided, cost and size of the modeling machine are increased. Additionally, tip calibration becomes more difficult. A single tip dispensing two different materials avoids calibration issues but introduces other problems. The tip needs to be purged of one material before the other material can be dispensed, in order to avoid mixing of dissimilar materials. Material as well as build time are wasted in purging the tip. Also, if any of a first material remains despite the purging effort, the remaining first material will contaminate the second material resulting in possible degradation of model quality.

None of the known methods for dispensing multiple materials from different material supply sources are entirely satisfactory. There is an unmet need for a dispensing technique that dispenses multiple types of modeling materials and is free from the disadvantages of the prior art.

BRIEF SUMMARY OF THE INVENTION

The present invention is a multi-tip extrusion method for building a three-dimensional object, whereby modeling materials from distinct supply sources are each deposited in a layerwise predetermined pattern from dispensers having co-planar dispensing tips. The tip spacing is controlled so that a road of material extruded by a leading one of the tips will cool and shrink from the plane of the tips before a trailing one of the tips passes over the extruded road. The trailing tip therefore does not smear the road. A minimum transit time between tips can be calculated as a function of road height and thermal diffusivity of the material forming the road. The method of the present invention avoids the smearing, calibration, reliability, cost and throughput issues of the prior art techniques, enabling efficient production of good quality models. Z.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front elevation of a first exemplary embodiment of an extrusion apparatus according to the present invention.

FIG. 2 is a left side elevation of an extrusion head which incorporates the extrusion apparatus of FIG. 1, with a portion shown in sectional.

FIG. 3 is a sectional view of a portion of the first exemplary embodiment of an extrusion apparatus, taken along a line 3—3 of FIG. 2.

FIG. 4 is an enlarged sectional view of the two tips of the extrusion apparatus of FIG. 3, shown in a dispensing mode.

FIG. 5 is a bottom plan view of a second exemplary embodiment of an extrusion apparatus according to the present invention.

FIG. 6 is a front elevation of a third exemplary embodiment of an extrusion apparatus according to the present invention.

FIG. 7 is a cross-sectional view of the nozzle of the extrusion apparatus of FIG. 6.

DETAILED DESCRIPTION

The multi-tip extrusion apparatus and design methodology of the present invention may be employed with respect to various types of modeling or prototyping systems which form three-dimensional objects by extruding solidifiable modeling material onto a base. Particularly applicable are those systems which utilize an extrusion head to deposit “roads” of material heated to be flowable, and which material shrinks and solidifies upon a drop in temperature to form a solid model. A preferred material deposition and build-up process is of the type disclosed in U.S. Pat. No. 5,121,329.

FIG. 1 shows an extrusion apparatus 10 according to the present invention, comprised of a pair of dispensers 12 and 14 carried by a body 16. Each of the dispensers 12 and 14 is adapted to receive and dispense material from a distinct material supply source, such as is illustrated in FIG. 2. In a typical modeling application, one of dispensers 12 and 14 will receive and dispense a modeling material, while the other will receive and dispense a support material. Alternatively, the materials may be modeling materials of different colors or having other diverse properties.

FIG. 2 shows an extrusion head 18 comprised of the extrusion apparatus 10 mounted to a carriage 20. The extrusion head 18 is electrically coupled to a system controller 21. As shown, the carriage 20 is movable in a horizontal plane along X and Y axes under control of the controller 21, to permit depositing the material in a known manner in successive layers onto a horizontal base movable along a vertical Z-axis (not shown). Alternatively, it is recognized in the art that any three-dimensional relative movement between the extrusion head 18 and the base may be implemented to form a three-dimensional object; In the embodiment shown, carriage 20 includes a conduit 22 which receives a strand of filament 24 from a supply spool (not shown) of a type known in the art. The filament 24 is formed of a solid material that is flowable when heated and that is to be used in forming a model or a support structure for the model. Carriage 20 additionally includes a pair of feed rollers 26 and 28, a motor 30 and a gear 32, which comprise a suitable filament feed mechanism of a type known in the art. The roller pair 26 and 28 controllably advance the filament strand 24 into the dispenser 12. As shown, roller 26 is a drive roller while roller 28 is an idler. Motor 30 drives the roller 26 via the gear 32. A second filament feed mechanism (not shown) is provided on carriage 24, supplying a filament strand to dispenser 14 from a different supply spool (not shown).

As shown in FIGS. 1–3, the pair of dispensers 12 and 14 are comprised of a pair of flow tubes 34, a nozzle 36 defining two separate flow channels 38, and a pair of co-planar discharge tips 40 of the nozzle 36. Each of the dispensers 12 and 14 define a separate and distinct flow path through the body 16. Each flow tube 34 has a receiving end 42 which defines an inlet to the flow path and a dispensing end 44 positioned to deliver a flow of material to one of the flow channels 38 of the nozzle 36. In the embodiment shown, the flow tubes 34 are thin-wall tubes of the type disclosed in U.S. Pat. No. 6,004,124. The flow tubes 34 are secured to the nozzle 36 such as by brazing. The flow tubes 23, the nozzle 36 and the body 16 are made of a heat conductive material, so as to enable maintaining the flow path at a temperature at which the material being supplied is flowable. The body 16 contains a heating rod 46 extending therethrough. Heating rod 46 is ohmically controlled by the system controller 21 to heat the body 16, which conducts heat to the flow tubes 34 and the nozzle 36. Where the material is supplied as a solid, as in the embodiment shown, the material is liquified in the flow tubes 34, and then flows through the nozzle 36 for dispensing. To monitor the temperature of the extrusion apparatus 10, a thermocouple may be utilized. A thermocouple 48 is shown positioned in the nozzle 36 between the flow channels 38, allowing careful monitoring of the discharge temperature of the material by the system controller 21. If the temperature gets too high, the system controller 21 can toggle off the heating rod 46.

The body 16 may be conveniently manufactured in multiple sections which are mechanically detachable to permit cleaning and replacement of the dispensers 12 and 14. As illustrated in FIG. 2, the body 16 has a back section 47 and a front section 49. The dispensers 12 and 14 clamp between the sections 47 and 49, in a manner similar to that described in U.S. Pat. No. 6,004,124.

As shown in FIGS. 3 and 4, each dispensing tip 40 defines a discharge orifice 50 through which molten material is extruded. Each discharge orifice 50 receives flowable material from one of the flow channels 38 of the nozzle 36. FIG. 4 illustrates the dispensing of extrudate material onto a base 52 by one of the tips 40, so as to build up a three-dimensional object. The base 52 may be a substrate approximating a plane on which models are built, or it may be previously deposited layers of modeling material. The material is extruded as a road 54 having a thickness h. As shown in FIG. 4, the extrusion head 20 carrying extrusion apparatus 10 is moving forward at a velocity v as material is extruded through the orifice 50 of the leading tip 40 and the trailing tip is idle.

In a typical application, the velocity v varies as the extrusion head 20 proceeds through a path comprising a start point, a stop point and multiple vertices. Each vertex is assigned a velocity v, representing the velocity at which the extrusion head 20 can be driven through that vertex without exceeding an allowable error. The extrusion head 20 preferably accelerates and decelerates between vertices so as to achieve a high throughput, in a manner such as is disclosed in U.S. Pat. No. 6,054,077.

As mentioned above, the tips 40 of the first exemplary embodiment are co-planar. The tips 40 each have a downward face 56 and the faces 56 are at the same Z-height. In practice of the present invention, typical manufacturing tolerances will result in the tip faces being in only approximately the same plane (i.e., approximately the same Z-height). Approximate co-planarity is acceptable within the tolerances given below. In reference to FIG. 4, each downward face 56 has an outer diameter d_(o) and an inner diameter d_(i) defining the orifice 50. The inner and outer diameter of the tips 40 may be the same, or these dimensions may be different, as desired for a given application. The centerline tip-to-tip spacing is given by the variable s_(c), while the spacing between the tip faces 56 is given by the variable s. According to the design methodology of the present invention, a minimum spacing between the tips 40 is mathematically predicted according to the tip geometry, build conditions and extrudate material of a given application, so that one tip will not smear the extrudate deposited by the other. The tip spacing requirements will now be described.

The material deposited is one which will solidify upon encountering a predetermined condition, such as the controlled temperature in a build envelope in which modeling takes place. Virtually all materials of interest shrink as they cool and solidify. According to the present invention, the spacing s between the tip faces 54 is greater than or equal to a predetermined minimum value which provides a predetermined time-lag Δt between the two tip faces 56. The spacing between the tips 40 is made great enough to allow extrudate material freshly deposited by the leading tip 40 to cool and shrink before the trailing tip 40 passes over it, so that the trailing tip 40 will not drag across and smear a road 54 that it did not extrude. This design overcomes the problem of the prior art broad-faced tips, wherein feature detail would be destroyed by the passing of a non-extruding tip surface. The minimum tip spacing can be calculated for a given tip geometry, build conditions and extrudate material. Before describing the mathematical analysis, the following additional parameters are first defined:

-   -   v_(min)=minimum tip velocity at a vertex     -   a_(max)=maximum tip acceleration     -   k_(e)=extrudate thermal conductivity     -   C_(p)=extrudate heat capacity     -   T_(e)=extrudate temperature emerging from tip     -   T_(g)=extrudate temperature upon relative solidification     -   T_(h)=build environment temperature     -   T(t)=extrudate temperature t seconds following its emergence         from the tip     -   α=extrudate thermal expansion coefficient     -   ρ=extrudate average density     -   k_(u)=air thermal conductivity     -   K_(e)=extrudate thermal diffusivity

The thermal diffusivity K_(e) is defined according to the equation: $\begin{matrix} {K_{e} = \frac{k_{e}}{{Cp}\;\rho}} & (1) \end{matrix}$

As the road 54 deposited by the leading tip 40 cools, it shrinks away from the z-plane of the tips. In order to prevent the trailing tip 40 from dragging across and smearing the road 54, the spacing s between the tip faces 56 is made great enough so that the road 54 should shrink sufficiently during the transit time between the two tips 40 as to leave a gap between the road 54 and the trailing tip face 56. According to the present invention, the spacing s is a distance calculated to result in at least a critical gap g_(c) between the trailing tip face 56 and the extruded road 54. We define the critical gap g_(c) as the amount of air between the trailing tip face 56 and the extruded road 54 that doubles the thermal resistance between the trailing tip face 56 and the center of the road (as compared to no gap). Using this definition, and assuming perfect co-planarity of tip faces 56, the critical gap may be expressed according to the equation: $\begin{matrix} {g_{c} = {\frac{h}{2}\;\left( \frac{k_{a}}{k_{e} - k_{a}} \right)}} & (2) \end{matrix}$

Additionally, the fractional expansion of the road thickness (i.e. g_(c)/h) is known to be equal to the product of the extrudate thermal expansion coefficient and the drop in extrudate temperature from the time it is deposited to the time the trailing tip 40 goes by. The drop in extrudate temperature required to create the critical gap may thus characterized by the following equation: $\begin{matrix} {{T_{e} - {T\;(t)}} = \frac{g_{c}}{h\;\alpha}} & (3) \end{matrix}$

The time required to create this change in temperature (ignoring air convection) can be calculated according to the equation¹: ¹ H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Science Publications, 2d ed., p. 98. $\begin{matrix} {{\Delta\; t} = \frac{0.3h^{2}}{K_{e}}} & (4) \end{matrix}$

Assuming that a corner is printed at the minimum tip vertex velocity, the criteria for the spacing between the tips becomes: $\begin{matrix} {{{v_{\min}\;\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}} \leq s} & (5) \end{matrix}$

Several observations can be made regarding tip spacing criteria in a three-dimensional fused deposition modeling system:

-   -   Spacing requirements increase linearly with minimum tip vertex         velocity.     -   Spacing requirements increase linearly with maximum tip         acceleration.     -   Spacing requirements increase quadratically with road thickness         for low acceleration gantries. Stated otherwise, decreasing the         road thickness offsets the effects of increasing velocity.     -   Spacing requirements increase as the fourth power of road         thickness for high acceleration gantries (a_(max)>2v_(min)/Δt).     -   Spacing requirements decrease with increasing extrudate thermal         conductivity.     -   Spacing requirements decrease as the temperature of the emerging         extrudate is increased, for a fixed build environment         temperature (more thermal shrink and faster temperature change).     -   Spacing requirements increase linearly with tip outer diameter         (since s=S_(c)−d_(o) for same-sized tips).     -   An acceptable manufacturing tolerance on the tip face         co-planarity is that the z-height of the tip faces (measured         along the center line of the orifices) may be offset a distance         approaching the critical gap g_(c). Within this tolerance range,         the trailing tip should have at least about a clearance fit with         the extruded road.     -   It is desirable to keep the tips as close together as the         criteria permit, as this will minimize impact of any nominal         tilt of the base from horizontal.         For some applications, it may be desirable to deposit more than         two different types of materials from the same extrusion head.         For such applications, the present invention can be utilized in         an embodiment having more than two tips, such as is illustrated         in FIG. 5. FIG. 5 shows a nozzle 60 having three tips 40. As         with the first exemplary embodiment described above, the tips 40         of nozzle 60 are integral with dispensers adapted to receive         material from three different material supply sources,         permitting the selective dispensing of any one of the three         materials. The tip spacing criteria derived with respect to the         first exemplary embodiment having two tips 40 applies also to         embodiments having three or more tips. Applying the spacing         criteria to an embodiment having three or more tips, the minimum         spacing between any two of the tips must satisfy equation 5.

EXAMPLE

An example is given in which theoretical results are compared to experimental results. In this example, the build conditions are that of a Stratasys FDM® three-dimensional modeling machine depositing ABS thermoplastic, according to the parameters given in Table 1 below:

TABLE 1 VARIABLE VALUE d_(o) 45 mils (1.14E-4 meter) d_(i) 12 mils (3.05E-4 meter) S_(c) 100 mils (2.54E-3 meter) h 10 mils (2.54E-4 meter) ν_(min) 0.9 ips (0.023 meter/sec) α_(max) 3 inches/sec² (7.77E-3 g's) k_(e) 1.4 watt/(meter ° C.) C_(p) 1.8 joule/(gram ° C.) T_(e) 270° C. T_(g) 140° C. T_(h) 70° C. α 8E-5/° C. ρ 1.1 gram/centimeter³ k_(a) 0.016 watt/(meter ° C.) The thermal diffusivity for the above example parameters, calculated according to equation (1), is 7.07E-7 meters²/sec. The critical gap, calculated according to equation (2), is 0.06 mils (1.5 microns). Applying equation (3), the change in temperature required to create the critical gap is predicted to be 72° C. The time required to create this change in temperature, predicted according to equation (4), is 27 milliseconds. Finally, equation (5) predicts that the spacing s between the tip faces should be greater than or equal to 0.025 inches. A nozzle having a spacing s of 0.065 inches was utilized on a Stratasys® FDM® three-dimensional modeling machine depositing ABS thermoplastic under the above example parameters. The model quality was observed to by unimpaired by the passing of the trailing tip.

A third exemplary embodiment of the present invention is shown in FIGS. 6 and 7. FIG. 6 shows an extrusion apparatus 70 having two dispensers 72 and 74 in a body 76, wherein the body 76 further includes a thermal insulator 78 and two heating rods 46. The thermal insulator 78 is positioned between the dispensers 72 and 74 to provide a degree of thermal separation between the dispensers. The two heating rods 46 are located on opposite sides of the thermal insulator 78. The dispensers 72 and 74 are of the same general type as dispensers 12 and 14 of embodiment one. The dispensers 72 and 74 share a common nozzle 82 which includes two dispensing tips 84. As is best shown in FIG. 7, the thermal insulator 78 is ambient air that fills a vertical channel 80 extending through the body 76 and the nozzle 82, and a horizontal channel 86 extending through the nozzle 82. The air insulator may be stagnant air or moving air. The thermal insulator 78 may alternatively be any insulating material that will provide a desired degree of thermal separation between the two dispensers. The thermal insulator 78 allows the dispensers 72 and 74 to be maintained at diverse temperatures by the heating rods 46. Two thermocouples 48 are thus utilized, one positioned in each of the dispensers 72 and 74. The thermal separation between the dispensers 72 and 74 provided by the third exemplary embodiment is useful where it is desirable to maintain the two extrusion materials at different temperature elevations, such as where the two materials have significantly different melting points. Again, the tip spacing criteria derived with respect to the first exemplary embodiment applies equally to the third exemplary embodiment.

Various modification may be made to the thermally-insulated embodiment shown in FIGS. 6 and 7 that will increase the temperature gradient between the two dispensers 72 and 74. For example, increasing the size of the channel 80 will provide a greater degree of thermal separation between dispensers 72 and 74 by increasing the volume of insulating air, as will boring channels through the body 76 to the exterior walls of the channel 80. It should further be understood that the body 76 and nozzle 82 can be physically separated into right and left sections by a solid insulator (e.g., a high temperature plastic or a ceramic material), to maximize the temperature gradient between the dispensers 72 and 74. It should be noted, however, that providing the nozzle as a single piece is advantageous provided that adequate thermal separation can be maintained, as calibration of tip position becomes an issue using a multi-piece nozzle. The thermally-insulated embodiment can be further modified to include three or more dispensers, with some or all of the dispensers thermally separated from one another, with each of the dispenser tips satisfying the spacing criteria.

Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. For example, it should be understood that while the present invention is shown and described herein as receiving modeling material in the form of a filament strand provided by a filament feed mechanism, the extrusion apparatus of the present invention can be utilized to advantage in modeling systems which receive other types of material feed stocks from other types of feed mechanisms, including liquid feed stocks. It will also be appreciated that various modifications may be made to the dispensers in keeping with the teachings of the present invention. The flow tubes, for example, could be eliminated by instead boring flow channels through the body itself. It will further be appreciated that innumerable other various modifications may be made to the extrusion apparatus of the present invention. 

1. A layered deposition method for building a three-dimensional object comprising the steps of: providing a first thermally solidifiable modeling material to a first dispenser, the first dispenser having a first dispensing tip which has a downward planar face; providing a second thermally solidifiable modeling material to a second dispenser, the second dispenser having a second dispensing tip maintained in a fixed vertical position relative to the first dispensing tip, the second dispensing tip having a downward face approximately co-planar with the face of the first dispensing tip; dispensing roads of the first material in molten form from the tip of the first dispenser onto a base contained in a build environment having a temperature lower than an extrudate temperature of the first and second material, while moving said first dispensing tip in a predetermined pattern within a layer above the base; dispensing roads of the second material in molten form from the tip of the second dispenser while moving said second dispensing tip in a predetermined pattern within the same layer; and controlling the dispensers such that a trailing one of the first and second dispensers lags behind a leading one of the first and second dispensers by no less than a minimum transit time Δt, defined as the time for a road deposited by the leading dispenser to sufficiently shrink due exclusively to cooling so that the tip of the trailing dispenser does not drag across and smear the road.
 2. The method of claim 1, wherein the minimum transit time Δt is given by the equation ${{\Delta\; t} = \frac{0.3h^{2}}{K_{e}}},$ where h is the height of the deposited road and K_(e) is the thermal diffusivity of the material forming the road.
 3. The method of claim 2, wherein the dispensing tips accelerate and decelerate through paths comprising multiple vertices and have a minimum vertex velocity v_(min) and a maximum acceleration a_(max), and wherein the dispensing tips are spaced apart a minimum spacing s characterized by the relationship ${{v_{\min}\;\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}} \leq {s.}$
 4. A layered deposition method for building a three-dimensional object comprising the steps of: providing a first thermally solidifiable modeling material to a first dispenser carried by an extrusion head, the first dispenser having a first dispensing tip which has a downward planar face positioned in approximately a z-plane; providing a second thermally solidifiable modeling material to a second dispenser carried by the extrusion head, the second dispenser having a second dispensing tip maintained in a fixed vertical position relative to the first dispensing tip, the second dispensing tip having a downward face spaced apart a distance s from the face of the first dispensing tip and approximately co-planar with the face of the first dispensing tip; moving the extrusion head at a controlled velocity in a layerwise predetermined pattern above a base contained in a build environment having a temperature lower than an extrudate temperature of the first and second material alternately dispensing roads of the first material in molten form from the tip of the first dispenser and dispensing roads of the second material in molten form from the tip of the second dispenser while the extrusion head is moved in the predetermined pattern within a layer; and controlling the velocity of the extrusion head such that a road deposited in the layer by a leading one of the first and second dispensing tips shrinks from the plane of the tips due exclusively to cooling before a trailing one of the first and second dispensing tips passes over the road, so that the trailing dispensing tip does not smear the road.
 5. The method of claim 4, wherein the extrusion head is controlled so that a minimum transit time Δt elapses between deposition of the road by the leading dispensing tip and the passing of the trailing dispensing tip, wherein Δt is a function of the height of the deposited road the thermal diffusivity of the material forming the road.
 6. The method of claim 5, wherein the dispensing tips accelerate and decelerate through paths comprising multiple vertices and have a minimum vertex velocity v_(min) and a maximum acceleration a_(max), and wherein the dispensing tips are spaced apart a minimum spacing s characterized by the relationship ${{v_{\min}\;\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}} \leq {s.}$
 7. A method for building a three-dimensional object in a modeling machine of the type which builds three-dimensional objects in layers by depositing thermally solidifiable modeling material as roads of molten material into a build environment having a temperature lower than an extrudate temperature of the material, and from an extrusion head that moves at a known speed in a predetermined cross-sectional pattern, the method comprising: providing a first thermally solidifiable modeling material to a first dispenser carried by the extrusion head, the first dispenser having a dispensing tip which has a downward planar face; providing a second thermally solidifiable modeling material to a second dispenser carried by the extrusion head, the second dispenser having a dispensing tip maintained in a fixed vertical position relative to the tip of the first dispenser, the dispensing tip of the second dispenser having a downward face spaced apart a distance s from the tip face of the first dispenser and approximately co-planar with the tip face of the first dispenser; dispensing roads of the first material in molten form from the tip of the first dispenser, without using a planarizer to shape the roads; dispensing roads of the second material in molten form from the tip of the second dispenser, without using a planarizer to shape the roads; moving the extrusion head in a layer according to a predetermined pattern, wherein each of the first and second dispensers at different times act as a leading and a trailing dispenser; and controlling the velocity of the extrusion head such that the trailing one of the first and second dispensers lags behind the leading one of the first and second dispensers by no less than a minimum transit time Δt, wherein Δt is the time for a road deposited by the leading dispenser to sufficiently shrink due to cooling so that the tip of the trailing dispenser does not drag across and smear the road.
 8. The method of claim 7, wherein the minimum transit time Δt is given by the equation ${{\Delta\; t} = \frac{0.3h^{2}}{K_{e}}},$ where h is the height of the deposited road and K_(e) is the thermal diffusivity of the material forming the road.
 9. The method of claim 8, wherein the dispensing tips accelerate and decelerate through paths comprising multiple vertices and have a minimum vertex velocity v_(min) and a maximum acceleration a_(max), and wherein the dispensing tips are spaced apart a minimum spacing s characterized by the relationship ${{v_{\min}\;\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}} \leq {s.}$
 10. A layered deposition method for forming a three-dimensional object, comprising the steps of: moving an extrusion head at a controlled velocity in a layer, said extrusion head carrying first and second adjacent dispensers; depositing a thermally solidifiable material in molten form in a road from a downward facing tip of the first dispenser into a build envelope having a temperature lower than an extrudate temperature of the material, while the extrusion head is moved; and controlling the velocity of the extrusion head such that when the second dispenser trails the first dispenser, a downward facing tip of the second dispenser approximately co-planar with the tip of the first dispenser lags behind the tip of the first dispenser by no less than a minimum transit time Δt, defined as the time for the deposited road to sufficiently shrink from the plane of the tips due to cooling so that the tip of the second dispenser does not smear the road.
 11. The method of claim 10, wherein the minimum transit time Δt is given by the equation ${{\Delta\; t} = \frac{0.3h^{2}}{K_{e}}},$ where h is the height of the deposited road and K_(e) is the thermal diffusivity of the material.
 12. The method of claim 11, wherein the first dispenser accelerates and decelerates through paths comprising multiple vertices and has a minimum vertex velocity v_(min) and a maximum acceleration a_(max), and wherein the dispensing tips are spaced apart a minimum spacing s characterized by the relationship ${{v_{\min}\;\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}} \leq {s.}$
 13. The process of claim 10, wherein the extrusion head further carries a third dispenser adjacent the first dispenser, and further comprising controlling the velocity of the extrusion head such that when third dispenser trails the first dispenser, a downward facing tip of the third dispenser approximately co-planar with the tip of the first dispenser lags behind the tip of the first dispenser by no less than the minimum transit time Δt.
 14. A layered deposition method for forming a three-dimensional object, comprising the steps of: moving first and second adjacent dispensers at a controlled velocity in a a layer, said dispensers having downward facing co-planar dispensing tips; depositing a thermally solidifiable material having a thermal diffusivity K_(e) in molten form in a road having a height h from the tip of the first dispenser while the first dispenser moves in a predetermined pattern, into a build envelope having a temperature lower than an extrudate temperature of the material; and controlling the dispensers such that the tip of the second dispenser does not pass over the road deposited by the first dispenser until the road shrinks due to cooling from the plane of the tips, such that the tip of the second dispenser does not smear the road.
 15. The method of claim 14, wherein the controlling step comprises trailing the tip of the first dispenser with the tip of the second dispenser at a distance of no less than s, wherein s is a function of the road height h and the thermal diffusivity K_(e) of the material forming the road.
 16. The method of claim 15, wherein s is given by v_(min) ${{\Delta\; t} + {\frac{1}{2}\; a_{\max}\;\Delta\; t^{2}}},$ wherein the first dispenser accelerates and decelerates through paths comprising multiple vertices with a minimum velocity at a vertex v_(min) and a maximum acceleration a_(max), and Δt is given by the equation ${\Delta\; t} = {\frac{0.3h^{2}}{K_{e}}.}$
 17. The method of claim 14, wherein the controlling step comprises trailing the tip of the first dispenser with the tip of the second dispenser by a minimum transit time Δt, calculated as a function of road height h and the thermal diffusivity K_(e) of the material forming the road.
 18. The method of claim 17, wherein the minimum transit time Δt is given by the equation ${\Delta\; t} = {\frac{0.3h^{2}}{K_{e}}.}$ 